Constrained decay of dynamo-generated magnetic fields

In many astrophysical systems, magnetic fields are grown and maintained by turbulent fluid motions in what is known as the fluctuation dynamo. What is the fate of the magnetic field when the sources of turbulence subside or become intermittent? Using a suite of visco-resistive MHD simulations, we investigate the decay of dynamically strong, folded magnetic fields, initialized organically from the saturated state of the fluctuation dynamo, through the lens of statistical invariants (Hosking & Schekochihin 2021). Once turbulent forcing subsides, magnetic folds unwrap and/or tear (depending on the Reynolds and Lundquist numbers), and the system relaxes into a magnetically dominated state. This state has local patches of net magnetic helicity and net magnetic flux left over from the fluctuation dynamo -- these quantities must simultaneously be conserved during decay. Because these dynamics are not solely constrained by helicity conservation, the decay of dynamo-generated fields is not governed solely by the Saffman helicity invariant, but also, we argue, by a formally analogous object related to conservation of magnetic flux. A corollary of this fact is that inverse transfer of energy to large scales during decay is suppressed relative to the case of fields without patches of net magnetic flux.